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Wolfram Summer SchoolFounded in 2003

16th Annual Wolfram Summer School, held at Bentley University June 24–July 13, 2018


Sibesh Kar

Wolfram Science

Class of 2015


Sibesh Kar is an undergraduate freshman majoring in physics at BITS Pilani, India. His primary interests and past projects lie broadly in the fields of quantum computing, embodied cognition, space settlement design, thermodynamics, and alternative energy.

His foray into cellular automata was an unusual one: having read a book on Indian mythology just after making his way through Wolfram's opus, A New Kind Of Science, Sibesh successfully spent a day figuring out how to simulate the complex labyrinthine battle formations depicted in said book using simple 1D CA rules evolved on a toroidal grid. This cemented his fascination with how simple instructions can translate into complex behavior, and he has since explored these ideas in the fields of robotics and fundamental physics.

Greatly influenced by Feynman's 1982 paper on "Simulating Physics with Computers," Sibesh looks forward to exploring in depth the quantum nature of complex systems.

In his free time, Sibesh draws comic strips and writes haikus behind dinner napkins.

Project: Applying Cellular Automata to Study Quantum Hamiltonians

We attempt to construct and visualize a quantum Hamiltonian for cellular automaton systems, with the intention of arriving at a Hamiltonian expression and densities that may be compared to those in bosonic, fermionic, and other quantum field theories[1]. While more complicated situations are inevitable in the world of grand theories, we start out by investigating some simple models of time-reversible cellular automata. There is sufficient evidence to show that cellular automata controlled by the Margolus rule can be computationally universal[2]. This means that any such automaton can be arranged in special subsets of states that obey the rule of any other computationally universal cellular automaton.

Useful models are obtained from systems that follow the Margolus rule, where the evolution equations of the entire system over discrete time steps are obtained by ordering the coordinates as follows: first update all even lattice sites, then update all odd lattice sites[3] (the order is immaterial). For this purpose, splitting a space-time lattice into the even and the odd sub-lattices is a trick having wide applications. It does not mean that we believe the real world is also organized in a lattice system, where such a fundamental role is to be attributed to the even and odd sub-lattices; it is merely a convenient tool for creating such models. Some systems have been formulated to mathematically approximate such Hamiltonians[3] (namely through Baker–Campbell–Hausdorff expansions), and our aim in this project would be to attempt to visualize the time-reversibility and conservation laws that are a feature of such cellular automaton systems.


  1. 't Hooft, G. (2010). Classical Cellular Automata and Quantum Field Theory. In Proceedings of the Conference in Honour of Murray Gell-Mann's 80th Birthday (1st ed., pp. 397-408). World Scientific. doi:10.1142/9789814335614_0037
  2. Miller, D. B., & Fredkin, E. (2005, May). Two-state, reversible, universal cellular automata in three dimensions. In Proceedings of the 2nd conference on Computing frontiers (pp. 45-51). ACM.
  3. 't Hooft, G. (2014). Reservoir Computing using Cellular Automata. arXiv:1405.1548 [quant-ph]